Preface Present era is most tough for highly aspirant youngersters mainly because of highly competitive environment all over the world and only toppers are preferred by employers, hence the competitive eaxaminations are organized for final selection. The general mathematics and aptitude has been the criteria to judge the ability of the candidates. Performance in the examination of the candidates is considered the most suitable parameter for final selection. Therefore candidates have to toil sinerely and honestly to get top ranks in the competitive examinations. I don’t know any other rout except hard work for success. At present, in most of the competitive examinations like Indian civil services, state civil services, banks, public and private organizations and other state examinatios for different posts, university entrance tests etc. are based on candidates’ ability in mathematics and general aptitude. It is quite common that number of coaching institutes are flourishing all over the country to prepare them for competitive examinations and in result they have to pay highly. Poor but intelligent students could not get equal oppportunty as they are unable to attend these coaching institutes because of unexpected high fee so they feel unfortunate to beat the examinations. This environment make them nervous and hopeless.This book will help and support to all aspiring youngers for competitive examinations. The book, ‘Basics of Mathematics and Aptitude’ has been designed in very simple way to cover most of the important area of general mathematics which covers like simplification, average, age calculation, time and work, area, ratio and proportion, HCF and LCM, interest and compound interest, percentage, profit and loss, speed and distance and boat and stream. These chapters are not only very important but also qualify to answer most of the related questions asked in various competitive examinations. Similarly aptitude test is also very common now-a-days, therefore, different area of aptitude like series, number system,analogy, blood relations and coding and decoding chapters have been covered as well as elaborated in this book to acquaint the students for various nature of questions most commonly asked in the examinations.The book is of an objective nature with multiple answers. The problems from simple to complicated in nature have been taken and solved with simple hints so that candidates can solve the problems easily and make them ready to excel in different examinations. In the end of each chapter, few questions with answers have been given for practice. It is a general advice to the students that they must go on for practice as practice makes people perfect.

The numerical based on simple mathematics like divide, multiply, sum, deduction, under root, percentage etc are given below to sharpen the inherent ability of the students. This simplication is a very good exercise to aqcquaint the students about basic mathmetics so that they can solve tough questions quickly. Therefore some tips are given below for solving the questions.

What is an Average ? The word “average” is used in everyday life to describe where the middle number of a data set is. It’s the typical number you would except to find in a series of numbers. In statistics, the average is called the “arithmetic mean” usually just shortened to the mean. Both the average and the mean use the same formula : Avg = total sum of all the numbers/ number of items in the set. In other word, to find the average, add up all of the numbers in the set, and then divide by however many items you have. Let’s say you have 5, 10, and 15. Add them all up to get 5 + 10 + 15 = 30, then divide by 3(the number of items). The answer is 30/3 = 10. In probability and statistics, you’ll see the following formula used

Aptitude questions related to ages are commonly asked in various competitive exams, so you should definitely solve few questions for exercise. Now let us go through the different types of statements used in this topic. Let us find the age of Rakesh by understanding his statement. Let us take the kid’s current age as X. So as per statement given by him, X = 1.5(X – 10). Solving for X, we get the value of X as 30. Hence current age of Rakesh’s son is 30 years.

Introduction It is a very important chapter as many questions are asked in competitive examination based on time and work relationship. This topic deals with the simultaneous performance involving the efficiency of an individual or a group and the time taken by them to complete a piece of work. Work is the effort applied to produce a deliverable or accomplish a task. A certain amount of time (T) is taken to complete a certain work (w). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = R x T Whenever some work is done, the total work itself can be taken as one unit. Hence, we assume the total work done as one unit in the problems we encounter in order to simplify the computations. In these cases, R = 1 / T or T = 1 / R. In other words, R and T are inversely proportional as R T = W, which is a fixed quantity.

The area of circle, rectangular, square, triangle, trapezium, rhombus,parallelogram etc are to be calculated by simple formulae but some times the combined area of more than two either circles or trapezium is difficult to calculate. It needs to understand the concept of area and how it is related to different planes. Some of the tips are given below to understand how to calculate the are a. Area A part of the plane enclosed by a simple closed figure is called a plane region and the measurement of plane region enclosed is called its area. Area is measured in square units. The different geometrical shapes formula of area and perimeter with examples are discussed below:

A pipe is connected to a tank or cistern. It is used to fill (inlet) or empty (outlet) the tank. Therefore, Inlet refers to a pipe which is connected to fill a tank is known as an inlet, while outlet refeRs to a pipe which is connected to empty a tank is known as an outlet. Generally the problems on pipes and cisterns are similar to problems on time and work. In pipes and cistern problems, the amount of work done is the part of the tank of filled or emptied. And, the time taken to do a piece of work is the time taken to fill or empty a tank completely or to a desired level. Following points should be remembered to solve the probles;

A ratio is the comparison or simplified form of two quantities of the same kind. This relation indicates how many times one quantity is equal to the other; or in other words, ratio is a number, which expresses one quantity as a fraction of the other. For example, the ratio of 1 to 2 is 1 : 2. The numbers forming the ratio are called terms. The numerator, “1”, in this case, is known as the antecedent and the denominator, “2”, in this case, is known as the consequent. In this article we will learn the approach applicable to solve various problems on ratios and proportions. In the next few lines you will go through some important concepts related to ratio problems and the methods you should apply to solve those problems. It is always better to solve as many problems as you can to boost your confidence. Some important points are given below to remember;

The H.C.F and L.C.M are very important and many questions are asked in almost all competitive examinations to judge the students ability and also capability to solve the problem. This concept is useful in the chapters of time and distance, time and work, pipes and cisterns, etc. The tricks used to find L.C.M and H.C.F of two or more numbers help in finding out quick solutions and thus reduce time during exams. L.C.M concept is important to solve problems related to racetracks, traffic lights, etc. H.C.F. concept is useful in calculating the largest size of tile/room in particular area, largest tape to measure the land, etc.

Simple interest? Simple interest can be simply defined as the interest that is paid only on the principal amount. Unlike compound interest, simple interest does not consider “interest on interest” concept and the value is obtained by multiplying the interest rate by the principal amount and the number of days that elapse between payments.

Basic Definitions Percent means ‘hundred’ and the sign % is read as percentage and x % is read as x percent. In other words, a fraction with denominator 100 is called a percent. In other words, “Percent” can be understood as “per 100” or “out of 100”. Percentage in itself is a dimensionless number used to tell how many parts per hundred are being considered. It is often denoted using the percent sign, “%”. The reference point for calculating percentage is taken as 100. For example, 20% means 20/100 (i.e. 20 parts from 100). This can also be written as 0.2.

Suppose you go to a Big Bazar to buy a shirt. You finalize the shirt and are shocked to see its price tag. The price mentioned on the sweatshirt is Rs. 2500. You ask the owner to give some discount. He offers a discount of 20%. Now just figure out, how much you will pay to the shopkeeper. Did you say 2000 rupees? You are bang on1 You will pay a sum after subtracting 20% of amount written on price tag i.e. Rs. 500 from Rs. 2500. You finally pay the shopkeeper 2500 – 500 = Rs. 2000. This example introduces you to the concept of marked price and discount. What you indirectly learned from this case is that the discount is calculated on the marked price only. Now let us assume here that the shopkeeper has purchased that sweatshirt for Rs.1600. How much money that shopkeeper has earned by selling this sweatshirt ? Now the shopkeeper has invested Rs. 1600 to buy this sweatshirt and finally sells for Rs. 2000. He makes a profit of Rs. 2000 – 1600 = Rs. 400 He earns this profit by putting in Rs. 1600. Thus his percentage profit is 100 x 400/1600 = 25%. This makes another concept of cost price and profit clear to you i.e. the price you put in from your pocket to buy a product is called cost price and the extra amount you get after selling the product is called the profit. The profit and loss percentage is calculated on cost price. Profit and loss problems are an integral part of all the competitive exams. You must understand the meaning of the basic terms used in profit and loss questions.

Time, Speed and Distance This section consists of problems on calculating speed, distance, time, head start and relative speed etc.

In most of the examinations, the questions related to boat and stream are asked. These questions are seemed to be very difficult but are very ticklish and easy to solve. The students need to concentrate on flow of stream upward and down ward. If the boat is moving towards the flow (downstream), the speed of boat and stream will be added and if the boat is moving towards opposite of stream flow (upstream), the distance covered by the baot will be equal to boat speed minus strean speed. Few important tips are given below to solve such type of questions. Downstream and Upstream Motion Downstream motion of a boat is its motion in the same direction as the flow of the river. Upstream motion is exactly the opposite. There are two parameters in these problems.

The questions related to different series like perfect squares, perfect cubes, geometric, arithmetic, two stage types etc. are given to quantify the aptitude of the students. These series have a definite pattern and require to stressed upon the basic knowledge and aptitude of the candidates to find out the proper answer. The series may follow different pattern either additive, deductive or multiple based on earlier values given in the series. Some of the tips are given below for better understanding of the students and also these tips will help you to solve some of the ticklish questions.

In mathematics, we use different type of digits called numbers. These numbers may be real, natural, rational, irrational, composite and complex, imaginary, perfect, positive and negative integers, whole number, prime and co prime numbers and even-odd numbers and make students confused. Therefore the concept of numbers should be very clear to the students so that they may answer the questions easily. The number system mainly into classified into 8 types.

Questions related to analogy ae simple to answer with application of little aptitude. Analogy means ‘similar items’. There is three types of Analogy, 1. Number Analogy, 2. Letter Analogy and 3. Word Analogy. In questions based on analogy, a pair of numbers/letters/words is given that have certain relationship between them. This pair is followed by a third numbers/letters/ words. The candidate is required to identify the relationship between the pair of numbers/letters/words given and find out the fourth numbers/letters/words such that the relationship between the third and the fourth numbers/letters/ words is similar to the relationship that exists between the first and the second numbers/letters/words. Similarly some figures are also given in questions and the next pattern of the figures is to be guessed. It requires candidate’s concentration and common wisdom. Therefore the candidates should be very attentive to answer these type of questions.

We must know our family, its members and their relationships. Let us first look at basic relationships which often figure in the questions. If you are conversant with the given items in the table below, half of your battle is already won. It is not required to mug-up these names, but instead make a clear picture in your mind as you go through each one of them. This will go a long way in retaining the details of these given shortcut tricks for solving Blood relations problems for logical and analytical reasoning. Read the following thoroughly before moving on

Introduction Almost every test of reasoning contains questions on coding. In such questions, generally one word and its code are given, and the students are required to find the code for the other word. The student is required to apply the same logic, as was applied in the given words. Let’s discuss some of the commonly asked questions based on coding : Some of the major types of coding logics are